Elements to be pushed = $n$
Elements to be popped = $m$
$m < n$
x = number of PUSH operations
y = number of POP operations
case 1: range of y
lower bound:
1. push m elements to stack S1
2. Pop m elements from stack s1.
3. push m elements on stack s2.
4. pop all m elements from stack s2.
Total pop operations happened here are $m+m = 2m$, hence $2m\leq y$
Upper Bound:
1. Push all n elements onto stack s1.
2. pop all n elements from stack s1.
3. push all elements on stack s2.
4. pop m elements from stack s2.
Total pop operations happened here are n+m, hence $y\leq m+n$
So far so good to eliminate the options (B) and (D).
Range of x:
lower bound:
1. push m elements to stack S1
2. Pop m elements from stack s1.
3. push m elements on stack s2.
4. pop all m elements from stack s2.
5. push remaining n-m elements on stack s2.
total push operations = $m + m + n - m = n+m$, hence $m+n \leq x$
So far so good to eliminate the option (C).
Upper Bound:
1. Push all n elements onto stack s1.
2. pop all n elements from stack s1.
3. push all n elements on stack s2.
4. pop m elements from stack s2.
Total PUSH operations = n+n, hence $x \leq 2n$
Hence, (A) is the correct choice.
PS: Don't know why is equal operator not given in any option.